WASHINGTON — Democratic Party officials agreed Saturday to seat Michigan and Florida delegates with half-votes, ruling on a long-running dispute that has threatened the party’s chances in November and maintaining Barack Obama’s front-runner status as he moves closer to the nomination.

The decision was a blow to Hillary Rodham Clinton as she was on the verge of watching Obama make history as the first black Democratic presidential nominee. It prompted an irate reaction from boisterous Clinton supporters in the audience and her chief delegate counter, Harold Ickes.

Ickes angrily informed the party’s Rules Committee that Clinton had instructed him to reserve her right to appeal the matter to the Democrats’ credentials committee, which could potentially drag the matter to the party’s convention in August.

The resolution increased the number of delegates needed to clinch the nomination to 2,118, leaving Obama 66 delegates short but still within striking distance after the three final primaries are held in the next three days.

The deal was reached after committee members met privately for more than three hours, trying to hammer out a deal, and announced in a raucous hearing that reflected deep divisions within the party.

“How can you call yourselves Democrats if you don’t count the vote?” one man in the audience shouted before being escorted out by security. “This is not the Democratic Party!”

Obama picked up a total of 32 delegates in Michigan, including superdelegates who have already committed, and 36 in Florida. Clinton picked up 38 in Michigan, including superdelegates, and 56.5 in Florida.

Obama’s total increased to 2,052, and Clinton had 1,877.5.

Proponents of full seating continuously interrupted the committee members as they explained their support of the compromise, then supporters of the deal shouted back.

“Shut up!” one woman shouted at another.

“You shut up!” the second woman shouted back.